How do I select the relevant features of the data?
Since you have all your data in a table, a relatively simple thing to do is to consider each column independently, and then seeing if the output variable (cost incurred) has a correlation to that.

If the column has no (or very low correlation) with the output variable, then consider it to be not important.  The ones that make the cut are then considered further.

This is obviously not very different from how a decision tree algorithm would work (such as ID3).